Laws of Sines and Cosines


If we have a triangle with angles α, β, and γ and sides a, b, and c opposite these angles respectively, then the following relationships hold.

Law of Sines

 a  =  b  =  c
sin αsin βsin γ


Law of Cosines

 a2  =  b2 + c2 − 2bc cos α
b2  =  a2 + c2 − 2ac cos β
c2  =  a2 + b2 − 2ab cos γ